Minimum Mean Absolute Percentage Error Research Articles

Forecasting system using single exponential smoothing with golden section optimization

Puri Wira Mahkota Ltd is a distributor company in the automotive parts industry. Puri Wira Mahkota has an obstacles in preparing weekly order on stock to the primary production unit. They predict total sales of product in the coming period just by using an expectation from stock administration staff then it will be compared with sales data in the previous period without any calculations using a definitive formula. Forecasting calculation could support Puri Wira Mahkota to predict the quantity of product. The purpose of this research is to apply the calculation process that can predict the quantity of product should be produced by the primary production unit every month and also to prevent over stock and out of stock. The method used in the forecasting calculation is Single Exponential Smoothing. To optimize Single Exponential Smoothing we used the Golden Section. The principle of the Golden Section is to reduce the alpha area boundary so it will produce an ideal forecast value with the minimum MAPE (Mean Absolute Percentage Error) level. This research shows the results that the Golden Section finds the optimal forecasting value with a level of MAPE (Mean Absolute Percentage Error) of 43.39%.

Price Behaviour and Forecasting of Onion Prices in Kurnool Market, Andhra Pradesh State

The objective of present study was to analyse the behaviour of onion prices in Kurnool market and forecasting the prices for the future. Based on secondary data from January 2003 to December 2017, the future prices were predicted for the months of January to June, 2018 by employing the Auto Regressive Integrated Moving Average (ARIMA) technique. The annual increase in prices of onion in Kurnool market was observed to be 6.22 per quintal per annum. The highest seasonal index was observed in the month of August and lowest seasonal index was recorded in May. Price cycles were not identified in onion prices. Maximum R-Square (62.34), minimum Mean Absolute Percentage Error (MAPE) (34.96), Root Mean Square Error (RMSE) (454.71) and Mean Absolute Error (MAE) (263.19) was used as a criteria to select the best model for price forecasting. Based on the above criteria the model (1, 1, 1) (1, 1, 1) was found to fit the time series to predict future prices. The forecasted price of onion would be ranging from 2956 to 1651 per quintal for the months from January to June 2018 respectively.

Design of LSTM-RNN on a Sensor Based HAR using Android Phones

Activity Recognition (AR) is monitoring the liveliness of a person by using smart phone. Smart phones are used in a wider manner and it becomes one of the ways to identify the human’s environmental changes by using the sensors in smart mobiles. Smart phones are equipped in detecting sensors like compass sensor, gyroscope, GPS sensor and accelerometer. Human Activity Recognition (HAR) framework collects the raw data from sensors and observes the human movement using different classification methods. This paper focuses for Activity Recognition (AR) based on smart phone by analyzing the performance of various Deep Learning (DL) approach using in-built gyroscope and accelerometers. In this work, HAR dataset can be utilized from UCI based Machine Learning repository. The sensors such as gyroscope and accelerator are used to record the signals and performs various activities namely walking- downstairs, walking-upstairs, jogging, standing, walking and sitting while a user wearing the smartphone in a pocket. The performance metrics has analyzed to recognize user’s activities using DL approach namely Recurrent Neural Network with Long-Short Term Memory (RNN- LSTM) were applied. The result provides 96% better accuracy for RNN-LSTM with minimum Mean Absolute Percentage Error (MAPE) when compare to other machine learning classifier.

FORECASTING OIL PALM PRODUCTION BASED ON A NONLINEAR AUTOREGRESSIVE EXOGENOUS (NARX) NEURAL NETWORK MODEL

time series data analysis and prediction tool that is able to predict the yield of oil palm is needed to ensure an acceptable forecasting quality. An attempt was made in this study to develop a Nonlinear Autoregressive Exogenous (NARX) neural network model of oil palm production using MATLAB. This NARX model was used to predict the yield of oil palm in the states of Kelantan, Johor, Sabah and Sarawak in Malaysia. The performance of the NARX model was tested and validated using the Levenberg-Marquardt (LM) training algorithm and was compared with the Autoregressive Integrated Moving Average (ARIMA) model. The best performance of the NARX model was achieved at 70 per cent: 15 per cent: 15 per cent, with 10 neurons in the hidden layers and a delay value of four for Sarawak. For Kelantan and Johor, the NARX model produced the best result using the parameters of 70 per cent:10 per cent:20 per cent, with 13 neurons in the hidden layers and a delay value of four. The best result for Sabah was achieved using the parameters of 70 per cent: 15 per cent: 15 per cent, with 13 neurons in the hidden layers and a delay value of four. The results demonstrated that the proposed NARX model was more effective in modeling and forecasting time series data than the ARIMA model. The NARX model registered a minimum mean square error and mean absolute percentage error with a maximum average accuracy percentage and correlation coefficient. Keywords: Oil palm cultivation, yield predictions, nonlinear autoregressive exogenous neural network, autoregressive integrated moving average.

NDVI time series stochastic models for the forecast of vegetation dynamics over desertification hotspots

ABSTRACTLand degradation in semi-arid natural environments is usually associated with climate vulnerability and anthropic pressure, leading to devastating social, economic and environmental impacts. In this sense, remotely sensed vegetation parameters, such as the Normalized Difference Vegetation Index (NDVI), are widely used in the monitoring and forecasting of vegetation patterns in regions at risk of desertification. Therefore, the objective of this study was to model NDVI time series at six desertification hotspots in the Brazilian semi-arid region and to verify the applicability of such models in forecasting vegetation dynamics. We used NDVI data obtained from the MOD13A2 product of the Moderate Resolution Imaging Spectroradiometer sensor, comprising 16-day composites time series of mean NDVI and NDVI variance for each hotspot during the 2000–2018 period. We also used rainfall measured by weather stations as an explanatory variable in some of the tested models. Firstly, we compared Holt-Winters with Box-Jenkins and Box-Jenkins-Tiao (BJT) models. In all hotspots the Box-Jenkins and BJT models performed slightly better than Holt-Winters models. Overall, model performance did not improve with the inclusion of rainfall as an exogenous explanatory variable. Mean NDVI series were modelled with a correlation of up to 0.94 and a minimum mean absolute percentage error of 5.1%. NDVI variance models performed slightly worse, with a correlation of up to 0.82 and a minimum mean absolute percentage error of 22.0%. After the selection of the best models, we combined mean NDVI and NDVI variance models in order to forecast mean-variance plots that represent vegetation state dynamics. The combined models performed better in representing dry and degraded vegetation states if compared to robust and heterogeneous vegetation during wet periods. The forecasts for one seasonal period ahead were satisfactory, indicating that such models could be used as tools for the monitoring of short-term vegetation states.

Efficient solar radiation estimation using cohesive artificial neural network technique with optimal synaptic weights

Estimation of solar potential is vital for renewable energy applications. In several studies, artificial neural networks have been employed to model solar radiation using various meteorological parameters. The collection and availability of the most appropriate input parameters is important for getting an accurate artificial neural network model. The present study aims to estimate the global solar radiation using different meteorological parameters and identify the significant parameters based on the analysis of synaptic weights in an artificial neural network model using the connection weight approach. Initially, artificial neural network and empirical models is applied to estimate the solar radiation in Chamba region. The artificial neural network architecture 5-48-15-1 resulted in minimum mean absolute percentage error of 12.15%. The mean absolute percentage error values for linear models are found to be 18.95%, 15.39%, and 21.62%, respectively. Thereafter, connection weight approach is applied to find significant parameters. The efficacy of the approach has been shown through a case study related to estimation of solar radiations in the Hamirpur region situated in the state of Himachal Pradesh (India). Five input parameters, namely temperature (T), relative humidity (RH), clearness index (KT), precipitation (PT), and pressure (P), have been considered to estimate solar radiations using a feed-forward neural network. The proposed approach infers that temperature is the most significant parameter followed by humidity and pressure. The clearness index and precipitation has been found to have the least effect on the estimation of solar radiations. Results also indicate that artificial neural network based technique is more accurate compared to empirical model.

Estimation of Solar Potential for Thailand Using Adaptive Neurofuzzy Inference System Models

This research paper proposes a new method of global solar radiation prediction for Thailand using adaptive neurofuzzy inference system (ANFIS) models. Contrary to mathematical-based modeling approaches, the proposed models are able to estimate the monthly mean of daily global solar radiation at the ground level without using the earth's atmospheric layer model. The proposed technique alternately utilizes the 9-year long recorded spatiotemporal data of solar irradiance from meteorological ground stations in the modeling process. With a limited number of ground stations, it covered six regions of Thailand, ANFIS modeling; testing and restructuring have been performed repetitively; and finally, the best-fit models with minimum mean absolute percentage errors (MAPEs) corresponding to six regions of Thailand are obtained. Moreover, the ANFIS models have been tested comparatively to the measured data and the multilayer feed forward artificial neural network (ANN) models, which has a good agreement to real data for the proposed models, can be met with the average accuracy of 7.07% MAPE. By applying this model as a tool to estimate solar potential, the local government or the business sector can provide basic information, which is useful for solar energy system planning and project development.

PARAMETER OPTIMIZATION OF SINGLE EXPONENTIAL SMOOTHING USING GOLDEN SECTION METHOD FOR GROCERIES FORECASTING

Department of Agriculture and Food Security Malang City, especially in the Field of Food Supply Availability and Distribution requires a reference forecasting of food prices in Malang. The method used in the forecasting calculation is Single Exponential Smoothing. In the process of calculating the Single Exponential Smoothing method, it takes alpha parameters between 0 and 1. The problem is when to estimate the alpha value between 0 to 1 with trial error with the aim of producing minimal forecasting results. Therefore, this study aims to determine the optimal alpha value. The method used in this research is the Golden Section Method. The principle of Golden Section method in this study is to reduce the boundary area so as to produce a minimum MAPE (Mean Absolute Percentage Error) value The data used in this study is the price of 9 commodities of Groceries in Malang since January 1, 2016 until December 31, 2017. The results showed that the Golden Section method found that the optimal alpha value was 0.999 with MAPE average of 9 commodities is 0.79%. So with this golden section method researchers do not need a long time to determine alpha by trial error

PARAMETER OPTIMIZATION OF SINGLE EXPONENTIAL SMOOTHING USING GOLDEN SECTION METHOD FOR GROCERIES FORECASTING

Department of Agriculture and Food Security Malang City, especially in the Field of Food Supply Availability and Distribution requires a reference forecasting of food prices in Malang. The method used in the forecasting calculation is Single Exponential Smoothing. In the process of calculating the Single Exponential Smoothing method, it takes alpha parameters between 0 and 1. The problem is when to estimate the alpha value between 0 to 1 with trial error with the aim of producing minimal forecasting results. Therefore, this study aims to determine the optimal alpha value. The method used in this research is the Golden Section Method. The principle of Golden Section method in this study is to reduce the boundary area so as to produce a minimum MAPE (Mean Absolute Percentage Error) value The data used in this study is the price of 9 commodities of Groceries in Malang since January 1, 2016 until December 31, 2017. The results showed that the Golden Section method found that the optimal alpha value was 0.999 with MAPE average of 9 commodities is 0.79%. So with this golden section method researchers do not need a long time to determine alpha by trial error

Neural-network based boost pressure prediction for two-stage turbocharging system of diesel engine

Abstract A boost pressure prediction research based on neural network is carried out for a diesel engine with two-stage adjustable turbocharging system. First, based on the co-simulation using GT-POWER and MATLAB/Simulink model, the dynamic influence of cycle fuel injection quantity and bypass valve opening of the turbine on boost pressure of diesel engine is studied. The boost pressure shows strong nonlinear relationship with the two aforementioned affecting parameters. Second, a nonlinear autoregressive neural network prediction model (NARXNN) with external input is designed to predict the boost pressure of the diesel engine. The cycle fuel injection quantity, bypass valve opening of turbine, and current boost pressure are used as the inputs of the neural network in order to predict the future boost pressure. Then the neural network prediction model is identified based on the mean absolute percentage error (MAPE). The identification results show that the minimum MAPE (3.52%) is achieved when the number of hidden layer nodes is 15. At last, the neural network prediction model for boost pressure is verified by simulation. The one-step prediction simulation results of boost pressure show that the established prediction model can accurately predict the boost pressure, and the MAPE of the verification data is 3.98%. And the multistep prediction simulation results show that the pressure prediction error in the 50-step prediction domain is within 0.05bar, which indicates that the prediction model has high accuracy.

Weight estimation for anesthetic administration using singular value decomposition and template matching for supine subject of different obesity levels

Weight estimation is an important parameter in different fields such as anesthetic dose calculations, Criminal Investigation, Nutrition expert and forensic field. This paper focused on medical applications which are necessary to know weight in different scopes like emergency department, Intensive Care Units (ICU), and operation rooms, to give patient correct drug dosage. This paper represents the estimating of weight using image processing techniques, singular value decomposition (SVD), template matching for the classification and surface fitting model. The results show that the most significant parameters in evaluating the body’s weigh are the area of the body’s trunk and the area of the upper arm. The resultant surface fitting polynomial fitting shows the minimum mean absolute percentage error (1.42%) smaller than all previous methods in the corresponding literature (9%–15%).The supine body’s position of the subject under study will enable the contribution of the obese belly in the dimension of the trunk, which makes this approach efficient in estimating the body’s weight for subjects of different abdominal obesity.

Application of SVR Models in Stock Index Forecast Based on Different Parameter Search Methods

Stock index forecast is regarded as a challenging task of financial time-series prediction. In this paper, the non-linear support vector regression (SVR) method was optimized for the application in stock index prediction. The parameters (C, σ) of SVR models were selected by three different methods of grid search (GRID), particle swarm optimization (PSO) and genetic algorithm (GA).The optimized parameters were used to predict the opening price of the test samples. The predictive results shown that the SVR model with GRID (GRID-SVR), the SVR model with PSO (PSO-SVR) and the SVR model with GA (GA-SVR) were capable to fully demonstrate the time-dependent trend of stock index and had the significant prediction accuracy. The minimum root mean square error (RMSE) of the GA-SVR model was 15.630, the minimum mean absolute percentage error (MAPE) equaled to 0.39% and the correspondent optimal parameters (C, σ) were identified as (45.422, 0.012). The appreciated modeling results provided theoretical and technical reference for investors to make a better trading strategy.

Probabilistic day-ahead system marginal price forecasting with ANN for the Turkish electricity market

This study presents a system day-ahead hourly market clearing price forecasting tool for the day-ahead (DA) market and a system DA hourly marginal price forecasting tool for the real-time market of the Turkish electric market (TEM). These forecasting tools are developed based on artificial neural networks (ANNs). A series of historical price data of the TEM are utilized to model and optimize the ANN structure and to develop the ANN-based price forecasting tool. The methodology used to select the optimum ANN architecture provides the minimum daily mean absolute percentage error for both day-ahead market prices in the TEM. Performances of the proposed ANN model and the multiple linear regression model in forecasting the day-ahead hourly market clearing price are compared. The proposed ANN model is modified using volatility analysis and the Bienayme-Chebyshev inequality in order to forecast system marginal prices probabilistically within a lower and an upper boundary.

CF-Kriging surrogate model based on the combination forecasting method

The spatial correlation function (SCF) is an important part of the Kriging surrogate model that describes the sample data structure, and the SCF affects the fitting accuracy of the Kriging surrogate model directly. In a Kriging surrogate model, a single SCF is typically selected to describe the sample data structure, which may cause sample information loss and fitting error. A new Kriging surrogate model for combination forecasting (CF-Kriging) was constructed by integrating of linear weighted approach based on the combination forecasting method, in which the differences in the sample information described by the diverse SCFs for the same sample data structure were considered. The integrity of the sample information of the CF-Kriging model was improved using single-SCF Kriging surrogate models as sub-models and considering the minimum mean absolute percentage error as the improved target for the fitting accuracy. The effectiveness of the CF-Kriging surrogate model was demonstrated using four test functions and two engineering problems, which indicated that the CF-Kriging surrogate model could effectively improve the fitting accuracy and the fitting stability of an ordinary Kriging surrogate model.

Wind speed forecasting based on wavelet packet decomposition and artificial neural networks trained by crisscross optimization algorithm

Wind speed forecasting is of great significance for wind farm management and safe integration into electric power grid. As wind speed is characterized by high autocorrelation and inherent volatility, it is difficult to predict with a single model. The aim of this study is to develop a new hybrid model for predicting the short wind speed at 1h intervals up to 5h based on wavelet packet decomposition, crisscross optimization algorithm and artificial neural networks. In the data pre-processing phase, the wavelet packet technique is used to decompose the original wind speed series into subseries. For each transformed components with different frequency sub-bands, the back-propagation neural network optimized by crisscross optimization algorithm is employed to predict the multi-step ahead wind speed. The eventual predicted results are obtained through aggregate calculation. To validate the effectiveness of the proposed approach, two wind speed series collected from a wind observation station located in the Netherlands are used to do the multi-step wind speed forecasting. To reduce the statistical errors, all forecasting methods are executed 50 times independently. The results of this study show that: (1) the proposed crisscross optimization algorithm has significant advantage over the back-propagation algorithm and particle swarm optimization in addressing the prematurity problems when applied to train the neural network. (2) Compared with the previous hybrid models used in this study, the proposed hybrid model consistently has the minimum mean absolute percentage error regardless of one-step, three-step or five-step prediction.

A better measure of relative prediction accuracy for model selection and model estimation

Surveys show that the mean absolute percentage error (MAPE) is the most widely used measure of prediction accuracy in businesses and organizations. It is, however, biased: when used to select among competing prediction methods it systematically selects those whose predictions are too low. This has not been widely discussed and so is not generally known among practitioners. We explain why this happens. We investigate an alternative relative accuracy measure which avoids this bias: the log of the accuracy ratio, that is, log (prediction/actual). Relative accuracy is particularly relevant if the scatter in the data grows as the value of the variable grows (heteroscedasticity). We demonstrate using simulations that for heteroscedastic data (modelled by a multiplicative error factor) the proposed metric is far superior to MAPE for model selection. Another use for accuracy measures is in fitting parameters to prediction models. Minimum MAPE models do not predict a simple statistic and so theoretical analysis is limited. We prove that when the proposed metric is used instead, the resulting least squares regression model predicts the geometric mean. This important property allows its theoretical properties to be understood.

Comparisons of GM (1,1), and BPNN for predicting hourly particulate matter in Dali area of Taichung City, Taiwan

This paper represents the first study to compare seven types of first–order and one–variable grey differential equation model [abbreviated as GM (1, 1)] and back-propagation artificial neural network (BPNN) for predicting hourly particulate matter (PM) including PMio and PM2.5 concentrations in Dali area of Taichung City, Taiwan. Their prediction performance was also compared. The results indicated that the minimum mean absolute percentage error (MAPE), mean squared error (MSE), and root mean squared error (RMSE) was 16.76%, 132.95, and 11.53, respectively for PM10 prediction. For PM2.5 prediction, the minimum MAPE, MSE, and RMSE value of 21.64%, 40.41, and 6.36, respectively could be achieved. All statistical values revealed that the predicting performance of GM (1, 1, x(0)), GM (1, 1, a), and GM (1, 1, b) outperformed other GM (1, 1) models. According to the results, it revealed that GM (1, 1) could predict the hourly PM variation precisely even comparing with BPNN.

Optimal estimator for uncertainty-based measurement quality control

This paper presents an optimal estimator for uncertainty-based measurement quality control. The optimal estimator is developed based on an acceptance probability approach under a risk balance criterion. It yields a balance between the false acceptance and false rejection when the measurement quality index is equal to unity. This paper also presents a minimum mean absolute percentage error (MAPE) estimator and a minimum mean squared percentage error estimator based on the frequentist decision-theoretic approach. The mathematical formulations for computing the MAPE, relative bias error (RBE), relative precision error (RPE), and root mean squared percentage error (RMSPE) of the three presented estimators and five existing estimators are derived. The performance of these estimators are compared and evaluated in terms of the false acceptance/rejection probability, MAPE, RBE, RPE, and RMSPE. Among the eight estimators considered, the presented optimal estimator is the most meaningful and the best estimator from the measurement quality control perspective.

An ERBF Network Prediction of Taiwan’s Crude Birth Rate Taking Economic Growth Rate and National Income Indices as Input Variables

In this study, exact radial basis function (ERBF) network was used to predict Taiwan’s crude birth rate (CBR), taking the economic growth rate (EGR) and national income indices (NII) as input variables. To establish the ERBF network model, the EGR and NII were taken as the input variables, and the CBR was taken as the output variable. The results indicated that the minimum mean absolute percentage error (MAPE), mean squared error (MSE), root mean squared error (RMSE), and maximum correlation coefficient (R) was 0.00 %, 0.00, 0.00, and 1.00, respectively when training. Those for testing were 52.41 %, 27.88, 5.28, and 0.00, respectively. According to the results, ERBF network could predict CBR by taking the EGR and NII as input variables.

Predicting air pollutant emissions from a medical incinerator using grey model and neural network

This paper represents the first study to use the grey model (GM) for predicting CO2, SO2 and O2 in the emissions from a medical incinerator. The artificial neural network (ANN) was also employed for comparison. Four control parameters were served as the input variables. The results indicated that two control parameters of temperature highly influenced air pollutant emissions. The minimum mean absolute percentage errors of 3.70%, 6.11% and 1.08% for CO2, SO2 and O2 could be achieved using GMs, meanwhile the minimum root mean squared errors for three air pollutant were 0.1660, 2.4521 and 0.2112. The control parameters could be applied to the prediction of air pollutant emissions. It also revealed that GM could predict the air pollutant emissions even though emission data were not sufficient.